改進(jìn)的乘積型核函數(shù)二次調(diào)頻信號(hào)的參數(shù)估計(jì)

李亞超 于勝韜 全英匯 邢孟道

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改進(jìn)的乘積型核函數(shù)二次調(diào)頻信號(hào)的參數(shù)估計(jì)

李亞超*于勝韜 全英匯 邢孟道

(西安電子科技大學(xué)雷達(dá)信號(hào)處理國防科技重點(diǎn)實(shí)驗(yàn)室 西安 710071)

該文提出一種基于改進(jìn)乘積型核函數(shù)的二次調(diào)頻信號(hào)的參數(shù)估計(jì)方法。首先，對(duì)信號(hào)乘以自身的共軛反轉(zhuǎn)并做相位匹配變換，通過積累后信號(hào)最大值位置得到信號(hào)的調(diào)頻率估計(jì)值；然后，再補(bǔ)償?shù)粼盘?hào)的調(diào)頻率，對(duì)解調(diào)頻(dechirp)后的信號(hào)構(gòu)造新的乘積型核函數(shù)，并變換到2維時(shí)間-時(shí)延域，沿時(shí)間和時(shí)延軸分別做相位匹配變換和傅里葉變換，在變換后的調(diào)頻率變化率-頻率平面通過最大值的位置即可同時(shí)得到調(diào)頻率變化率和中心頻率的估計(jì)值，對(duì)補(bǔ)償?shù)粝辔坏男盘?hào)取均值并求模得到幅度值，從而實(shí)現(xiàn)二次調(diào)頻信號(hào)的參數(shù)估計(jì)和重構(gòu)。可見，該方法避免了對(duì)所有相位參數(shù)的迭代搜索，提高了運(yùn)算效率。最后，對(duì)單分量和多分量二次調(diào)頻信號(hào)的仿真結(jié)果證明了該方法的有效性。

信號(hào)處理；乘積型核函數(shù)；二次調(diào)頻信號(hào)；參數(shù)估計(jì)；相位匹配變換；FFT

1 引言

因此，針對(duì)以上問題，本文提出了一種基于改進(jìn)乘積型核函數(shù)的多分量QFM信號(hào)的參數(shù)估計(jì)方法，先估計(jì)信號(hào)的調(diào)頻率，再同時(shí)估計(jì)信號(hào)的調(diào)頻率變化率和中心頻率，最后估計(jì)信號(hào)的幅度，從而重構(gòu)原信號(hào)。仿真結(jié)果證明了該方法的有效性。

2 QFM信號(hào)的時(shí)頻分布

考慮單分量的QFM信號(hào)，表示為

或[15]

經(jīng)過變換后所得到的信號(hào)相位為

則信號(hào)對(duì)應(yīng)的PWVD為

3 基于乘積型核函數(shù)的QFM信號(hào)的參數(shù)估計(jì)

針對(duì)QFM信號(hào)，構(gòu)造一種新的乘積型的變換核函數(shù)：

將式(3)代入式(8)得

可以看出單分量QFM信號(hào)經(jīng)過該變換后仍具有最佳的時(shí)頻聚集性。

將式(7)得到的瞬時(shí)頻率曲線改寫為

3.1 單分量QFM信號(hào)的參數(shù)估計(jì)

信號(hào)形式如式(3)所示，首先構(gòu)造函數(shù)：

將式(3)代入，得

對(duì)式(13)做相位匹配變換

然后，將式(13)代入，得

對(duì)新的信號(hào)式(17)作式(8)所示的變換，得到

對(duì)式(18)做相位匹配變換得

3.2 多分量QFM信號(hào)的參數(shù)估計(jì)

再做相位匹配變換為

現(xiàn)有的如PHMT和PGCPF方法都是順序估計(jì)信號(hào)的三次項(xiàng)，二次項(xiàng)和一次項(xiàng)系數(shù)。由于低次項(xiàng)系數(shù)的估計(jì)是在高次項(xiàng)估計(jì)并補(bǔ)償之后進(jìn)行的，因次高次項(xiàng)系數(shù)的估計(jì)精度會(huì)影響低次項(xiàng)的估計(jì)精度，并且三次項(xiàng)系數(shù)的估計(jì)值是在構(gòu)造高階核函數(shù)(PHMT構(gòu)造6階核函數(shù)，PGCPF構(gòu)造4階核函數(shù))得到的，信噪比門限會(huì)比較高。與PHMT和PGCPF方法不同，本文的方法先通過構(gòu)造2階核函數(shù)(式(12)和式(25))估計(jì)二次項(xiàng)的系數(shù)，信噪比門限更低，在多分量信號(hào)情況下可以更好地檢測并估計(jì)信號(hào)的參數(shù)，新的乘積型的變換核函數(shù)(式(8)和式(34))保證了三次項(xiàng)的系數(shù)和一次項(xiàng)的系數(shù)分別沿時(shí)間軸和時(shí)延軸彼此獨(dú)立，因此可以同時(shí)估計(jì)三次項(xiàng)和一次項(xiàng)的系數(shù)，這樣可以避免高次項(xiàng)的估計(jì)精度對(duì)低次項(xiàng)的估計(jì)精度的影響，可見，本文的方法具有一定的優(yōu)勢。

3.3 QFM信號(hào)參數(shù)估計(jì)的實(shí)現(xiàn)

多分量QFM信號(hào)的離散化表達(dá)形式為

多分量QFM信號(hào)的參數(shù)估計(jì)步驟為：

步驟2 構(gòu)造式(25)的離散函數(shù)

為了更好地抑制旁瓣，可以選用其他的窗函數(shù)[22]來替代式(43)中的矩形窗。

步驟8 計(jì)算剩余信號(hào)能量

剩余能量與原信號(hào)能量的比值為

4 仿真分析

仿真1 為了驗(yàn)證乘積型核函數(shù)自身對(duì)外部交叉項(xiàng)的抑制能力，現(xiàn)取信號(hào)為

直接對(duì)信號(hào)進(jìn)行步驟4的操作，結(jié)果如圖1所示，通過峰值點(diǎn)的位置即可估計(jì)原信號(hào)的調(diào)頻率變化率和中心頻率，可以看出，兩分量能夠很好地分離，很好地抑制了外部交叉項(xiàng)的干擾，能實(shí)現(xiàn)信號(hào)各分量的參數(shù)估計(jì)。

表1 QFM信號(hào)真實(shí)值

表2 信噪比條件下QFM信號(hào)估計(jì)值

表3 信噪比條件下QFM信號(hào)估計(jì)值

表4 信噪比條件下QFM信號(hào)估計(jì)值

當(dāng)信號(hào)分量個(gè)數(shù)較少且信噪比較高時(shí)，本文提出的方法與PHMT和PGCPF方法的估計(jì)精度相差不大，但是當(dāng)分量個(gè)數(shù)較多或者多分量信號(hào)的二次項(xiàng)系數(shù)差別較小時(shí)，本文提出的方法具有更為準(zhǔn)確的估計(jì)結(jié)果，為此對(duì)兩種情況下參數(shù)估計(jì)性能分別進(jìn)行驗(yàn)證。

圖2 信噪比下多分量QFM信號(hào)在調(diào)頻率變化率-頻率平面的3維分布圖

表5 QFM信號(hào)真實(shí)值

5 結(jié)束語

本文針對(duì)多分量QFM信號(hào)提出了一種基于乘積型核函數(shù)的參數(shù)估計(jì)方法。該方法首先構(gòu)造核函數(shù)估計(jì)QFM信號(hào)的調(diào)頻率參數(shù)，接著補(bǔ)償?shù)粼盘?hào)的調(diào)頻率，接下來通過構(gòu)造新的乘積型的核函數(shù)將信號(hào)變換到2維時(shí)間-時(shí)延平面，在時(shí)間-時(shí)延平面分別沿時(shí)間和時(shí)延方向做相位匹配變換和FFT，將信號(hào)變換到新的2維調(diào)頻率變化率-頻率平面。在新的平面通過信號(hào)最大值的位置即可同時(shí)得到原信號(hào)的調(diào)頻率變化率和中心頻率的估計(jì)值。當(dāng)原信號(hào)由多分量構(gòu)成時(shí)，結(jié)合CLEAN技術(shù)逐漸分離并最終重構(gòu)所有的二次調(diào)頻信號(hào)。最后，仿真結(jié)果驗(yàn)證了本文提出的方法在估計(jì)多分量QFM信號(hào)參數(shù)方面的有效性。

圖4 多分量QFM信號(hào)的估計(jì)結(jié)果

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李亞超： 男，1981年出生，副教授，碩士生導(dǎo)師，研究方向?yàn)槔走_(dá)信號(hào)處理﹑SAR成像及信號(hào)檢測.

于勝韜： 男，1989年出生，碩博連讀生，研究方向?yàn)樾盘?hào)檢測、參數(shù)估計(jì)和雷達(dá)成像.

全英匯： 男，1981年出生，副教授，碩士生導(dǎo)師，研究方向?yàn)槔走_(dá)信號(hào)處理﹑SAR成像及實(shí)時(shí)信號(hào)處理.

邢孟道： 男，1975 年出生，教授，博士生導(dǎo)師，研究方向?yàn)槔走_(dá)成像和目標(biāo)識(shí)別等.

Parameter Estimation of Quadratic Frequency Modulated Signal Based on Improved Product Kernel Function

Li Ya-chao Yu Sheng-tao Quan Ying-hui Xing Meng-dao

(,,710071,)

A new method for estimating parameters of quadratic frequency modulated signals is proposed basing on a product kernel function. Firstly, the signal is multiplied by its conjugate reverse signal with the phase-matching transformation being performed, and then the estimated value of the chirp rate can be obtained by searching one-dimension maximum position of accumulated signals. Secondly, the chirp rate of the signal is compensated and a new product kernel function for the dechirped signal is structured to transform it into the two-dimensional time-lag domain, and the phase-matching transformation and FFT respectively are performed along time and lag axis. As a result, by the maximum searching in the new change rate of the chirp rate-frequency domain after transformation, the estimated values of both the change rate of the chirp rate and the center frequency can be obtained, with the phase of the signal being able to compensated and the amplitude estimated by calculating the magnitude of its average, thereby leading to the reconstruction of the signal. It is shown that the proposed method precludes the iterative search of all phase parameters and improves the operational efficiency.Finally, the paper presents the simulated results that confirm the effectiveness of this method.

Signal processing; Product kernel function; Quadratic frequency modulated signals; Parameter estimation; Phase-matching transformation; FFT

TN911.7

A

1009-5896(2014)11-2621-07

10.3724/SP.J.1146.2013.01578

李亞超 ycli@mail.xidian.edu.cn

2013-10-14收到，2014-07-03改回

國家自然科學(xué)基金(61001211, 61303035)，航空基金(20110181004)和中央高校基本科研業(yè)務(wù)費(fèi)(K5051202016)資助課題